# How do you identify all asymptotes or holes and intercepts for #f(x)=(2x^2-18)/(x^2-16)#?

##### 1 Answer

There are no holes. The VAs are

#### Explanation:

Given

find all asymptotes, holes and intercepts.

Factor the numerator and denominator.

A hole exists when the numerator and denominator contain the same factor (a factor "cancels out"). This function has no holes.

To find the vertical asymptote(s) (VA), find the values of

Set each factor of the denominator equal to zero and solve.

To find the horizontal asymptote(HA), compare the degree of the numerator and denominator. If the degrees are the same, the HA is the ratio of the leading coefficients.

For

the degree in both numerator and denominator is

The HA is

The

The

The

The

graph{(2x^2-18)/(x^2-16) [-10.04, 9.96, -3.56, 6.44]}